сократите дробь (3c+3d-2)/ 2d-2c+3c2-3d2. Created by vikaryzhenkova. algebra-ru

2d-2c+3c2-3d2...

November 2021 1 6 Report

сократите дробь (3c+3d-2)/ 2d-2c+3c2-3d2

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kolobok1431 $\frac{3c + 3d - 2}{2d - 2c +3c ^{2} - 3d ^{2} }$
Преобразуем знаменатель
2d - 2c + 3c²  - 3d² = (2d - 2c) -  (3d²  - 3c² ) = 2*(d - c) - 3*(d² - c²) =
= 2 (d - c) - 3*(d² - c²) = 2 (d - c) - 3*(d - c) * (d + c) =
= (d - c) * (2 - 3 * (d + c)) = (d - c) * (2 - 3c - 3d) =
= (d - c) * (- (-2 + 3c + 3d) ) =
= (c - d) * (3c + 3d - 2))
Подставив в дробь последнее значение знаменателя, получим
$\frac{3c + 3d - 2}{2d - 2c +3c ^{2} - 3d ^{2} }$ = $\frac{3c + 3d - 2}{(c - d)*(3c + 3d - 2)}$ = $\frac{1}{c - d}$
Ответ:   $\frac{1}{c - d}$

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